contents were fully presentable to the senses and in that respect altogether real.
And necessary, as Philippe de Vitry allowed, when their purpose was to make perfect a diminished
fifth or an augmented fourth. As we know, a certain provision of this kind was made by the earliest
theorists of harmony, when they incorporated B-flat into the modal system alongside B for use in
conjunction with F.
But when an E was written against the B-flat, one had to go outside the system to harmonize it. And
that was musica ficta. The required E-flat was not conceptualized as we might conceptualize it, as an
inflection of E. Instead, it was conceptualized as the upper member of a melodic semitone, D–E, for
which a solmization —mi–fa—could be inferred. So the E a semitone above D was a fa, which placed it
in an imaginary or “feigned” (ficta) hexachord with ut on B. Since the flat sign was itself a variant of the
letter “B” to denote a B that was sung fa (in the “soft hexachord” on F) instead of mi (in the “hard
hexachord” on G), so the flat sign in and of itself denoted fa to a musician trained to sing in hexachords.
Thus a flat placed next to an E did not mean “sing E a half step lower,” it meant “sing this note as fa.” The
result may have been the same so far as the listener was concerned, but understanding the different mental
process by which the E was deduced by the singer will make clear the reason why in most cases musica
ficta did not have to be expressly indicated by the composer with accidentals. In many contexts the
chromatic alteration was mandated by rule, and the rule was fully implied in the solmization, and so any
singer who thought in terms of solmization would make the chromatic adjustment without being
specifically told to do so, and, it follows, without even being aware of the adjustment as “chromaticism.”
It was not a deviation from a pure diatonic norm, it was a preservation of pure diatonic norms (in
particular, perfect fourths and fifths) where they were compromised by a well-known kink in the diatonic
system.
Musica ficta introduced to preserve perfect intervals was musica ficta by reason of (harmonic)
necessity (in Latin, causa necessitatis), and was considered perfectly diatonic. Just as automatic, and
diatonic, was musica ficta by long-established conventions—conventions that have left a trace on familiar
harmonic practice in the form of the “harmonic minor.” They mainly affected the Dorian mode, the one
closest to our minor mode. For example, there was a rule that a single B between two A’s had to be a B-
flat (and, though it rarely required any adjustment, that an F between two E’s had to be F natural).
Singers learned this rule as a Latin jingle: una nota super la / semper est canendum fa (“One note
above la is always sung fa”). This adjustment had the effect of lowering the sixth degree of the Dorian
scale, turning it into a sort of appoggiatura or upper leading tone to fifth degree, A, the note that formed
the boundary between the principal segments of the scale. (And it turned the Dorian scale, for all practical
purposes, into the minor scale.) It was a grammatical rule, not an expressive device; it was called into
play automatically, and so it did not need to be written down.
There was a similar rule affecting lower neighbors to the final in Dorian cadences. Such notes were
common enough in Dorian melodies to have a name: subtonium modi, as we may recall from chapter 3.
The rule about neighbors raised the subtonium, a whole step below the final, to the subsemitonium, a half
step below. The effect was similar to that of borrowing a leading tone in the minor mode and served the
same purpose, strengthening the grammatical function, so to speak, of the cadence. By signaling a more
definite close it made the final more “final.” For this purpose the auxiliary pitch had to be raised, not
lowered, thus forming the lower note in a mi–fa pair. To indicate it, a sign was needed that would instruct
the singer to “sing mi.” That sign, #, which we call a “sharp,” was originally derived from the “square B”
or b quadratum that functioned specifically as mi in the “hard hexachord.” In places like Dorian
cadences, where the subsemitonium modi or leading tone was called for by the routine application of a
rule, it again could “go without saying.” It did not need to be explicitly notated, though (like necessary
flats) it could be notated and frequently, if haphazardly, was.